1/2x=13-4/5x

Solution for 1/2x=13-4/5x equation:

1/2x=13-4/5x

We move all terms to the left:

1/2x-(13-4/5x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-4/5x+13)=0

We get rid of parentheses

1/2x+4/5x-13=0

We calculate fractions


5x/10x^2+8x/10x^2-13=0

We multiply all the terms by the denominator


5x+8x-13*10x^2=0

We add all the numbers together, and all the variables

13x-13*10x^2=0

Wy multiply elements

-130x^2+13x=0

a = -130; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-130)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-130}=\frac{-26}{-260}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-130}=\frac{0}{-260}
=0
$